Population grows according to the equation , where k is a constant and t is measured in years. If the population doubles every 10 years, then the value of k is
(a) 0.069 (b) 0.200 (c) 0.301 (d) 3.322 (e) 5.000
Hello,Originally Posted by frozenflames
the growth of this population can be described by the equation:
$\displaystyle p=p_{0} \cdot 10^{k\cdot t}$
where p is the actual amount, $\displaystyle p_{0}$ is the starting value.
Put in the values you know:
$\displaystyle 2 \cdot p_{0}=p_{0} \cdot 10^{k\cdot 10}$
$\displaystyle 2 = 10^{k\cdot 10}$
solve for k:
$\displaystyle log(2) = k\cdot 10$
now you have to use a caculator or a logarthmic table.
You'll get $\displaystyle k\approx .030103$
that means that none of the given results seem to be right.
Greetings
EB
Hello, RichB.Originally Posted by Rich B.
of course you are right - BUT. when frozenflames referred to the equation I was not aware, that the equation was meant which you used. It all depends on the base you choose for solving this problem. I have choosen for 10 and thats why I came up with a "wrong" result.
Have a nice day too.
EB
In fact it does not matter (in principle) what you take for $\displaystyle b$Originally Posted by earboth
(as long as it is positive ) in a growth equation of the form:
$\displaystyle
p(t)=p(0)b^{kt}
$
for:
$\displaystyle
p(t)=p(0) c^{\log_c(b)\ kt}
$
Here there is a good case for using 2 since we are discussing doubling
times, so here it might be natural to use:
$\displaystyle
p(t)=p(0)2^{kt}
$
RonL